Finite Group Databasebeta

← #46835408

Subgroups — #46835408

Order 34688.

202 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31774528C211yesmaximal, characteristic
2#31774233C212yesmaximal
3#31773836C211yesmaximal, characteristic
4#31773635C212yesmaximal
5#324×C271C211yesmaximal, characteristic
6#22576159—22no—
7#22576151—22no—
8#22576139—21no—
9#22576139C2212yes—
10#22576119—21no—
11C2×C4⋊Dic271C2211yescharacteristic
12#22576094—22no—
13#22576085—22no—
14C271⋊#95—21no—
15C271⋊#95—21no—
16C271⋊#95C2211yescharacteristic
17C2×C4⋊C4×C271C2211yescharacteristic
18C22⋊C8×C271C2212yes—
19C2×Dic542—21no—
20C2×Dic542D412yes—
21C22×Dic271—21no—
22C22×Dic271—21no—
23C4⋊Dic271—21no—
24C4⋊Dic271—21no—
25C4⋊Dic271—21no—
26C4⋊Dic271—22no—
27C4⋊Dic271D412yes—
28Dic271⋊C4—22no—
29Dic271⋊C4—22no—
30C22⋊Dic271—22no—
31C4×Dic271—22no—
32C22×C4×C271D411yescharacteristic
33C22×C4×C271D411yescharacteristic
34C22×C4×C271C2311yescharacteristic
35C2×C8×C271—22no—
36C4⋊C4×C271—22no—
37Dic542—42no—
38Dic542—81no—
39C2×Dic271—22no—
40C2×Dic271—22no—
41C2×Dic271—41no—
42C2×Dic271—41no—
43C2×Dic271—42no—
44C2×Dic271—41no—
45C2×Dic271—41no—
46C23×C271C2×D411yescharacteristic
47C2×C4×C271—21no—
48C2×C4×C271—21no—
49C2×C4×C271—21no—
50C2×C4×C271—41no—
51C2×C4×C271—41no—
52C2×C4×C271Q1612yes—
53C2×C4×C271C2×D412yes—
54C8×C271—42no—
55C22×C271—21no—
56C22×C271—21no—
57C22×C271#12011yescharacteristic
58C22×C271C2×Q1611yescharacteristic
59C22×C271#13711yescharacteristic
60C4×C271—22no—
61C4×C271—22no—
62C4×C271—41no—
63Dic271—42no—
64Dic271—42no—
65Dic271—81no—
66Dic271—81no—
67C2×C271—21no—
68C2×C271—21no—
69C2×C271#45111yescharacteristic
70C2×C271#45411yescharacteristic
71C2×C271#45811yescharacteristic
72C271#161711yescharacteristic, complemented, Sylow
73#1617—2711nomaximal, Sylow
74#544—2711no—
75#484—2712no—
76#400—2711no—
77#328—2712no—
78#324D27111yescharacteristic
79C4⋊Q8—5422no—
80#125—5422no—
81C22⋊Q8—2712no—
82C22⋊Q8—5421no—
83#117—5421no—
84C2×C4⋊C4—2711no—
85C2×C4⋊C4C2×D27111yescharacteristic
86#107—5422no—
87#103—5422no—
88C22⋊C8C2×D27112yes—
89#95—2711no—
90#95—5421no—
91#95—5421no—
92C2×Q8—2712no—
93C2×Q8—5421no—
94C22×C4—5421no—
95C22×C4—5421no—
96C22×C4D108411yescharacteristic
97C22×C4D108411yescharacteristic
98C22×C4C22×D27111yescharacteristic
99C2×C8—22no—
100C4⋊C4—22no—
101C4⋊C4—2712no—
102C4⋊C4—5421no—
103C4⋊C4—5421no—
104C4⋊C4—5422no—
105C4⋊C4—5421no—
106C4⋊C4—5422no—
107C4⋊C4—5422no—
108C22⋊C4—5422no—
109C42—5422no—
110C23C2×D108411yescharacteristic
111Q8—10842no—
112Q8—21681no—
113C2×C4—21no—
114C2×C4—21no—
115C2×C4—21no—
116C2×C4—41no—
117C2×C4—41no—
118C2×C4—5422no—
119C2×C4—5422no—
120C2×C4—10841no—
121C2×C4—10841no—
122C2×C4—10842no—
123C2×C4—10841no—
124C2×C4—10841no—
125C2×C4Dic108412yes—
126C2×C4D4×D27112yes—
127C8—42no—
128C22—21no—
129C22—21no—
130C22#2257613011yescharacteristic
131C22C2×Dic108411yescharacteristic
132C22#2257619311yescharacteristic
133C4—22no—
134C4—22no—
135C4—41no—
136C4—10842no—
137C4—10842no—
138C4—21681no—
139C4—21681no—
140C2—21no—
141C2—21no—
142C2#3177405511yescharacteristic
143C2#3177407211yescharacteristic
144C2#3177408811yescharacteristic
subgroupG/H
centerC22#22576130
commutator, cosocleC22×C4×C271C23
FrattiniC22×C4C22×D271
Fitting#324×C271C2
socleC22×C271#120
prime radicalC23×C271C2×D4
hypercenter#324D271
hypocenterC271#1617
LCSG ▷ C22×C4×C271 ▷ C22×C271 ▷ C271
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
72. C271#1617semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#317745282
#317742332
#317738362
#317736352
#324×C2712
#1617271